Session F11: Nematicity in Fe-based Superconductors

Ising nematic quantum critical point in a metal: a Monte Carlo study

The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP.   

NMR evidence for inhomogeneous nematic fluctuations in BaFe$_2$(As$_{1-x}$P$_x$)$_2$

We present evidence for nuclear spin-lattice relaxation driven by glassy nematic fluctuations in isovalent P-doped BaFe$_2$As$_2$ single crystals. Both the $^{75}$As and $^{31}$P sites exhibit stretched-exponential relaxation similar to the electron-doped systems. By comparing the hyperfine fields and the relaxation rates at these sites we find that the As relaxation cannot be explained solely in terms of magnetic spin fluctuations. We demonstrate that nematic fluctuations couple to the As nuclear quadrupolar moment and can explain the excess relaxation. These results suggest that glassy nematic dynamics are a universal phenomenon in the iron-based superconductors.   

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

The elastoresistivity tensor $m_{ijkl}$ relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement.   

Origin of the in-plane resistivity anisotropy of the iron pnictides: scattering rate or plasma frequency?

The prime experimental tool to probe the electronic nematic phase in the iron pnictides is the in-plane resistivity anisotropy, which can arise from an anisotropic scattering rate and/or an anisotropic plasma frequency. To shed light on its origin, we investigate the impact of spin fluctuations on the anisotropic ac conductivity of the iron pnictides. We show that two mechanisms contribute to the ac conductivity anisotropy. On the one hand, the inelastic scattering by spin fluctuations directly introduces an anisotropic scattering rate. On the other hand, the same inelastic scattering causes the renormalization of the Fermi velocity at the hot spots. Interestingly, while both mechanisms affect the ac conductivity anisotropy, only the first causes an anisotropy in the dc limit. In contrast, the second mechanism effectively renormalizes both the plasma frequency and the scattering rate. The latter effect opposes the anisotropy induced by the direct scattering of electrons, effectively reducing the observable scattering rate anisotropy. Our results agree qualitatively with recent experiments in detwinned iron pnictides and show the unavoidable entanglement between the scattering rate anisotropy and the plasma frequency anisotropy that arises from spin fluctuations.   

Nematic Crossover in BaFe2As2 under Uniaxial Stress

The nature of the nematic order in iron-based superconductors has invoked intense research interest. A substantial portion of experimental attempts on resolving this issue required the use of single-domain samples produced under external stress. Here we use Raman scattering, a technique that can detect spontaneous point-group symmetry breaking without resorting to single-domain samples, to study BaFe2As2, the parent compound of the “122” Fe-based superconductors. We show that an applied compression along the Fe-Fe direction, which is commonly used to produce untwinned orthorhombic samples, changes the structural phase transition at temperature Ts into a crossover that spans a considerable temperature range above Ts. Even in crystals that are not subject to any applied force, a distribution of substantial residual stress remains, which may explain phenomena that are seemingly indicative of symmetry breaking above Ts. Our results are consistent with an onset of spontaneous nematicity only below Ts.   

Neutron scattering in detwinned SrFe$_{2}$As$_{2}$ single crystals

\textbf{Abstract}:Large SrFe$_{2}$As$_{2}$ single crystals (2cm) were grown with self-flux method. The basic sample characterizations were described by XRD, MPMS and PPMS. Orthorhombic $a$ along horizontal orientation and $b$ along vertical orientation were determined by X-ray Laue diffraction. The crystals were cut into rectangular pieces along the [1,1,0] and [1,-1,0] directions by high precision wire saw. The device for sample detwinning was made of 6061 aluminum alloy with low neutron incoherent scattering cross section. Uniaxial pressure can be applied by a spring along orthorhombic [0,1,0] direction by tuning the screw in one end. The pressure can be calculated by the known elasticity coefficient (k $=$ 10.5 N/mm) and the compression of the spring ($\Delta $x) [1]. Our neutron scattering experiments were carried out using the MAPS at the ISIS in England. Low Energy (such as Ei$=$80meV) with different temperatures ,especially around (TN $=$ Ts $=$ 193 K) is done in the time-of-fight experiment[2]. It is interesting to find out the pressure induced spin excitation anisotropy. After careful analysis,we conclude that resistivity and spin excitation anisotropies are likely intimately connected. The results also compared with similar experiment in parent BaFe2As2 in Murlin at the ISIS. \textbf{Keywards:} neutron scattering, detwin, SrFe$_{2}$As$_{2}$, single crystals Figure 1, Large SrFe$_{2}$As$_{2}$ single crystals grown with self-flux method. References: [1] Xingye Lu \textit{et al.}, Science 345, 657 (2014). [2] Pengcheng Dai, Rev. Mod. Phys.~87, 855(2015).   

Nematic fluctuations and acoustic phonon in the Raman response of iron-based superconductors

Nematicity is a generic feature in the under- and optimally-doped iron-based superconductors. Raman and shear modulus studies indicate a critical behavior of the xy symmetry susceptibility towards an extrapolated temperature $\theta$ defining a hidden critical point tens of degrees below the structural transition $T_S$. It was proposed that Raman scattering is insensitive to the orthorhombic lattice deformation and a strong electron-phonon (ep) coupling could possibly lift the nematic transition from $\theta$ to $T_S$, while the ep coupling strength remains unknown. Here we report a very low frequency phonon mode associated with an orthorhombic lattice deformation near $T_S$ contributing to the xy symmetry Raman response. We propose an ep coupling model to describe the Raman response and establish the connection of Raman susceptibility and elastic shear modulus. The ep coupling strength deduced from the Raman response is insufficient to lift $T_S$ by 60~K above $\theta$, suggesting that the structural phase transition at $T_S$ and the hidden phase transition at $\theta$ have different origins.   

Electronic Raman study of superconducting Ba$_{1-x}$K$_x$Fe$_2$As$_2$

We use electronic Raman scattering to probe the superconductivity gap structure and collective modes in under-doped and optimally-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$. In the under-doped samples, we observe a sharp superconducting coherence peak at 60 cm$^{-1}$ in the XY (B$_{2g}$) geometry below $T_c$, which is consistent with the gap value determined by ARPES on the outer hole Fermi surface pocket \footnote{Nat. Commun. \textbf{2}, 394 (2011)}. The Raman spectrum shows a threshold at approximately 30 cm$^{-1}$ followed by the superconducting coherence peak with a low-energy tail. We identify a peak at around 95 cm$^{-1}$ between 13 K and 22 K in the same geometry in the orthorhombic phase below $T_c$, which becomes broader and weaker upon heating. A sharp and symmetric mode at 120 cm$^{-1}$ is also observed in the optimally-doped samples in the same geometry. These collective modes have similar energy scale with the neutron spin resonance mode, the kink observed by ARPES and the bosonic mode observed by STM \footnote{Nature \textbf{456}, 930 (2008); PRL \textbf{102}, 047003 (2009); PRL \textbf{108}, 227002 (2012)}, indicating that they have intimate relationship with superconductivity in the iron pnictides.   

Numerical Study of Iron-Based Superconductors and Nematic Order

We perform an exact diagonlization study of the multi-orbital Hubbard model including coupling to lattice degrees of freedom.The single-particle spectral function, dynamical spin, charge, and Raman response are studied to examine a spin nematic phase due to a biquadratic exchange coupling.   

The realization of nematic order in iron-pnictide superconductors

The interplay between the nematicity and superconductivity in iron-pnictide is studied with a proposed magnetic configuration in a microscopic model. The spin-driven order in the nematic state has been found in a small area in the electron-doped regime. In the nematic state, in the normal state, the broken degeneracy of the orbitals $d_{xz}$ and $d_{yz}$ causes the elliptic Fermi surface. In the state where the nematicity coexists with the superconductivity, an orthorhombic magnetic fluctuations appears and its Fourier transformation shows two uneven pairs of peaks at $(\pm\pi,0)$ and $(0,\pm\pi)$. Finally, two modulated stripe SDW perpendicularly intertwined each other and makes the charge density and the spatial distribution of the LDOS reflcting a $d_{x^2-y^2}$-symmetry form factor.   

Spin-Driven Nematic Instability in Realistic Microscopic Models: Application to Iron-Based Superconductors

Electronic nematicity due to the partial melting of density waves is a prevalent phenomenon in the field of high temperature superconductivity. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven order cannot be captured by the standard RPA method. By including fluctuations beyond RPA, we derive the orbitally-resolved nematic susceptibility of a generic multi-orbital Hubbard model, thus putting it on equal footing with other electronic susceptibilities of weakly and moderately interacting systems. Application to iron-based superconductors reveals that the $d_{xy}$--orbital plays a primary role in promoting a nematic transition preempting the magnetic transition. It furthermore demonstrates the importance of high-energy magnetic fluctuations in stabilizing nematic order in the absence of magnetic order. Finally, we show that the RPA ferro-orbital susceptibility shows no divergence on its own, providing strong evidence for a magnetic mechanism for nematicity.   

Effect of Orbital Nematicity on Superconductivity in the Iron Pnictides and Chalcogenides

Orbital ordering leading to the observed nematic phase in the iron-based superconductors has been firmly established in a variety of experiments. It is therefore important to investigate the effect of the orbital order on the superconductivity. To this end, we have performed strong-coupling calculation within the slave-boson approach to the multiorbital $t$-$J_1$-$J_2$ models for the iron-based superconductors. We report the phase diagram as a function of both electron/hole doping and the orbital ordering strength. We find that the amplitude of the otherwise dominant $A_{1g}$ ($s\pm$) pairing channel diminishes as the strength of orbital ordering is increased, yielding to the $B_{1g}$ ($d_{x^2-y^2}$) pairing channel. This effect is especially pronounced in the electron-doped case, with the $d$-wave pairing stabilized by the realistic values of the orbital splitting $\sim 50$ meV. While the $d$-wave pairing has not been conclusively observed in the iron-based superconductors, the competition between the $s$- and $d$-wave pairing found in the calculations may have ramifications for FeSe, KFe$_2$As$_2$ and K$_x$Fe$_{2-y}$Se$_2$.   

Possible surface nematic order in iron pnictides

Nematic fluctuations play important role in the physics of the iron-based superconductors. Indications for weak precursor nematic transition has been found in the compound BaAs$_{2-x}$P$_x$Fe$_2$$[$1$]$. However, high-resolution specific-heat measurements did not reveal any bulk transition$[$2$]$. To resolve this controversy, we consider the possibility of the surface nematic transition preceding the bulk transition. We consider the simplest model of two interacting quasi-two-dimensional electronic bands and explore the free-surface effects on the nematic order. We found that three-dimensional effects suppress the bulk nematic order and therefore this order is enhanced near the surface.\\ $[$1$]$Kasahara, S., et al. "Electronic nematicity above the structural and superconducting transition in Ba(As$_{1-x}$P$_x$Fe$)_2$." Nature 486.7403 (2012): 382-385.\\ $[$2$]$Luo, X., et al. "Antiferromagnetic and nematic phase transitions in Ba(As$_{1-x}$P$_x$Fe$)_2$ studied by ac microcalorimetry and SQUID magnetometry." Physical Review B 91.9 (2015): 094512.